Image Processing: Mathematics, Engineering, Or Art?

Abstract

From the strict mathematical viewpoint, it is impossible to fully achieve the goal of digital image processing, which is to determine an unknown function of two dimensions from a finite number of discrete measurements linearly related to it. However, the necessity to display image data in a form that is visually useful to an observer supersedes such mathematically correct admonitions. Engineering defines the technological limits of what kind of image processing can be done and how the resulting image can be displayed. The appeal and usefulness of the final image to the human eye pertains to aesthetics.Effective image processing necessitates unification of mathematical theory, practical implementation, and artistic display. Figure 1 shows the basic elements of any imaging scheme. The fundamental purpose of imaging is to convey information about the object to the observer, usually a human being. The measurements obtained at the input stage of imaging can assume various forms. They might consist of spatially separated samples of the luminosity of visibly detectable light, as in light photography. IntroductionOr, as is most often the case in medical imaging, the measurements might be of nonvisual quantities, such as x -ray intensity, the strength or time delay of sonic pulses, or the intensity of radiation being emitted by the object. In the newest form of medical imaging, that of nuclear magnetic resonance, the measurements involve a complex arrangement of magnetic and radiofrequency fields and the quantities being imaged are closely related to the density of the nuclei under study in combination with the relaxation times of the nuclear spins.Between the measurements and the display of the final image, some form of processing takes place.In photography or film -based radiography, the processing consists in film development. We will be more concerned here with digital image processing in which the measurements are manipulated by a digital computer.In order to emphasize the unity of the processing and display stages of imaging, we will assume the term "image processing" comprises both.It is typically desired that the observer synthesize the displayed information in order to draw a conclusion (make a diagnosis) about the object. Thus, the available information should be presented to the observer in such a way that he can most readily interpret it. Presently, the most efficient way to present the human observer with a vast amount of correlated information is through his visual sense. Thus, we will assume the end product of image processing is a visual image or picture. It is the purpose of imaging to provide an observer, usually a human being, information about the object under study. The information content is fundamentally limited by the measurements taken. Image processing, which naturally includes both the processing and display stages of the imaging chain, should convey as much of that information as possible in a form useful to that observer. From the strict mathematical viewpoint, it is impossible to ful...